21 ideas
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |